Friday, February 6, 2009

Another Story Involving Bad Math, Bad Science

I found the article Green Guru in a facebook post. It is from the publication First Things: The Journal of Religion, Culture and Public Life and was posted on February 2, 2009 by Stephen M. Barr.

Mr. Barr claims that,
"...if no one had more than two children, as the green guru would want it, the fertility rate could probably not be gotten above 1.4. In twenty generations the world population would plunge to less than 2 million."
This is 'voodoo math'. The error should be obvious by looking closely at what Barr is claiming. If the growth rate remains positive, then the population grows. When the growth rate declines, population growth slows. A population declines when the growth rate is negative. In other words, there is a big difference between the rate declining and the population declining. (Please comments.)

Mr. Barr should read 'The Population Bomb', 1968, by Dr. Paul Erlich, a Stanford University biologist, and 'The Population Explosion', 1990 by Paul and Anne Erlich. These books explain population growth in a manner that a lay person can understand. The math involved, in understanding population growth, can be understood by the average high school student.

To see how the basics of population growth works, see the illustration above. It is representative of the growth of a fictional family over a 100-year period, following the rule, mentioned by Mr. Barr, that a couple limits itself to begetting 'replacements' and thus has only two children.

The first couple, Andrew and Alana are born in 1900 and have two offspring, Brian and Bertha, around 1925. The family reproduces according the the 2-child rule for the rest of the century. Anyone familiar with rudimentary mathematics, sees the structure of '2 to the nth power' (an exponential function) as the basis for the population growth in this example. Alas, people die. The names in lavender, represent people who have perished.

In this example, there are 23 more people on the planet in the year 2000, compared to 1900. The rate of growth is 23 people per hundred years (0.23% per annum).

To compare the fictitious example to real life examples, we can look to the CIA who keeps statistics on population growth throughout the world. Their definition of Population Growth is as follows:
The average annual percent change in the population, resulting from a surplus (or deficit) of births over deaths and the balance of migrants entering and leaving a country. The rate may be positive or negative. The growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure (e.g., schools, hospitals, housing, roads), resources (e.g., food, water, electricity), and jobs. Rapid population growth can be seen as threatening by neighboring countries.
Referring to the chart below which uses 2008 statistics, we can see that, even accounting for war, the population growth rate in Afganistan is 3 times the rate in the U.S. The growth rate in the Gaza Strip is almost 4 times that of the U.S. The actual rate for the U.S. is almost 4 times the rate of our fictional family. The lowest rate, in this chart, is that of Russia. The growth rate in Russia indicates a population decline, as stated previously.

Mr. Barr states later in his article:
"Judging from remarks that colleagues have made in my presence, there are a remarkably many otherwise intelligent people who agree with the green guru that it is irresponsible to have more than two children, and who pride themselves on having stopped at two, as though they were benefiting society thereby. I suspect that this widespread attitude, based on an elementary mathematical error, may be one reason for the woefully low birthrates in economically advanced countries."

Oh really Mr. Barr! I think you might want to rethink your analysis.


Anonymous said...

Barr is referring to the fertility rate being 1.4, NOT the growth rate.

MathChique said...

Thank you Anonymous. Good point!
The fertility rate is the average number of births per woman.
The growth rate is how fast a population is growing.
They are somewhat related but not the same thing.
I still don't agree with Mr. Barr's argument. His math is still incorrect, namely this statement:
"...if no one had more than two children, as the green guru would want it, the fertility rate could probably not be gotten above 1.4. In twenty generations the world population would plunge to less than 2 million."
The 'fertility' rate in China is less that 1.4 and its populaton has still continued to grow.

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